Multiplying linkage



Feb. 21, 1950 A, SVQBODA 2,498,309

MULTIPLYING LINKAGE Filed April 1, 1946 3 Sheets-Sheet 2 INVENTOR ANTONIN SVOBODA ATTORNEY Patented Feb. 21, 1950 o STAT PATIENT Q FFICEL MULTIPLYING LINKAGE Antonin S'voboda, Cambridge; Mass: Application ApriL:1;1946, Serial No. 658,59.7"

2Claims:' Cl. 235-61) This: invention .relatesitoha. multiplyingilinkage andam'orecparticularly, to such. a linkage. of Tth'e plus, plus-minushtype.ina-whichn.thedispleicement' of onemembersis. a. single ivaluedenonslinear function of the product .iofrtherdi'splacement .of. two. other .numbers. The mechanism, whichlhave invented; determines,.. the product. ofi two indee pendent variables one, otwhichi. may. be I either i positive .ornegativeandithe other. of which'lmay be positive, for best; precision For? general. information purposes .in. connectionwith .th'epresentvinvention reference is made to the textbook; Computing, Mechanisms and I I inkagesrvol. 2.7, by.Antonin Svob'oda, Massachusettslnstituteof Lllchholdgy; Radiationliabbra l.

tony Series,cfiistfleditionil98; ,McGraw-Hillf'Book' Company, Inc.

An object of this invention is to provide a mechanical computer for determining the product" of two independent variables;

Another object oi -this invention "is to-provide a mechanical computer for"determining the prodnot of two independent variables; one -ofwhich" I may be either"positive-orinegativeand the other" of which is positive incharactrywhidh wlll "auto--- matically provid the--proper1sign* to :thesproductia of the variables-being1multlplle ilg A further object of-this invention isto provida mechanical computer having threew slfdable members and a: linkage systemoperativeIY connesting the members; in whim -the relative d1 and guiding isectionnillustratedyin Fige2'j'andi' .Fig.j. 5 is a side; elevation of the output section illustratedginFig.2.-

A vmechanism.embodying@my; invention...which is based on this discovery comprisestalinkaget having;- the necessary :critical relative; dimension 2:- that the displacement" of one of the members closely approximates theproductof thedisplzicment oi two other members of the device. In order to. make v.th'e nature of "my inventionclear, I TwilLfstate the critical. relationships referred [tol and describe the difie'rent mechanisms incor-s porating itin,further detaill.

Fig. 1. shows the generalarrangementof the mechanism ..and"indicates. that lit includes ;thr.ee'f pivoted 'orswinging members and an 'arm" pivotedlto afiized supportilfl"atthreepivots A; B, and CI respectively. Asli'deamember'ibll sli'clablytmount'ed upon. a shaft '60 ;as a meansfor introducin rbneof the variablefunbtions; the? product of" which. when: multiplied by a' second. variable function is to be determined by the fd'- vice... A'pair. of links.3"| and 32 pivotally mounted to members 30.."andf at. points.D' and E respec tively h'ave th'eihfr'tee ends joinedLby a-plvot'con; nection E. Alink 33has theopposite ends there oi.p ivo tally, connectedtolpoint Gof member If. and..to,point E'as shown; A'slidememberrllis operativelv connected tolmember 20 by means :of alinktafh'aving pivotconnections at points 'ls' and respectively, this slide. member; prcwiding'1;- a means for introducing the:secondvariableiunc= tion :into .the linkage. Point J of arm 40 "oper ati'vely, connected to; member 30 at 'point' l means. of a. link'. 10.; having ,ipivot connections at eachlend. Asecondflink 80. has one end'thereot pivotal-1y,.c0nnected'to pointK'ofFmember lli the; opposite. end fiof member 8Ubeing;pivotally"con necteditoiaslide member 8i .at pointM. Ifwe. allow. unity. (1 to be thebasis' ofbomparisomthe; relative. dimensions of. the various. linkages and swinging;,members.of.tlfe device are such that movementfof member 8] is a function of'the prod? uctiofntlie .movement ofjmemb'ers 21 .and. 50' rev spectively. The .crlticalrelative. dimension of. the various partsiofitheimechanism areasfollowsz' Horizontal distancetfromipivot pointBto' piv'otipoint'CL 33991;? Vertical distance from 1 pivot. point "B' to"' pivot point CL Vertical distance from." pivot point B" to.

pivot pointA'; 32371" Horizontal "distance from pivot point B" to pivotpoint A; Vertical distance from pivotpointBito'the c axis 'of'travelof "slide block 5L 3Z'750'1'j'1" Horizontal distance. fromthhpoint where the variable introduced by slide block' 50"equalsTzero to point Al 114095;

Length of 'memberlll alongthe line 5---..-315000'fl Angle included between line AG and line AH of member 20 Length of member 30 along the line BD Length of member 30 along the line BI Angle included between lines BD and B1 of member 30 Length of link 3| Length of member 32 Length of member 33 Length of member 40 from pivot point C to pivot point J The total length of member 40 may be designated by the letter R, the only requirement being that the dimension R be greater than 1.7000, since it does not enter into the actual multiplying operation, but only changes the proportionality constant of the XY product. Length of member 10 connecting points I .and J of members 30' and 40, respectively 4.5000

In the operation of the device, slide block 2| maybe considered to be an X input member, the horizontal displacement of which constitutes the X input. Similarly, slide box 50 may be considered to be a Y input member, the horizontal displacement of which constitutes the Y input. For multiplication of X and Y, slide block 2| and slide block 50 are positioned as desirable and the output will be proportional to the product of the X and Y. displacements. More specifically the output described is .8831R XY, where R is, as shown, the total length of arm 40. The dimensions and orientation of the linkage members listed above are such that the X and Y input scales are linear in nature. The XY product output scale is also uniform, the displacement of the slider 8| being directly proportional to the product of X and Y. Assuming that the X and Y input scales are uniformly graduated in feet from ljto l0, and the X and Y sliders are respectively positioned at 2 and 4, the output scale will be uniformly graduated such that it will indicate the value 8, after the factor .8831R has been taken into consideration.

AS previously mentioned the dimension of R may be any value greater than 1.7000, whereby the proportionality factor .8831R may be any value as determined by the desired movement of the slider 8|. Reference is now made to Fig. 2, which is an isometric drawing of the invention in more generalized form than that illustrated in Fig. 1. This embodiment of the invention may be easily considered in terms of an X input section, a Y input section, and locus determining means'for a product point D, and an output section. Section M constitutes the X input section. Section N is the Y input section together with the locus determining means, and section is the output section. While the functional operation of the embodiment shown in Fig. 2 is similar to that shown in Fig. 1, this latter embodiment differs from that of Fig. 1 in that it is constituted of three frameworks M, N, and 0, having shafts 2|, and 22 rotatably mounted in supports 23, 24, and '25, respectively, as means for operatively connecting the various linkages associated with each of the frameworks. In addition, triangular member 20 of Fig. 1 has been replaced by members 21 and 28 of Fig. 2, rigidly joined by shaft 2|.

These links 21 and 28 are equivalent to triangle 20 in that they are rigidly joined to shaft 2| and therefore will rotate to the same angle in respouse to rotation of shaft 2 I. Similarly, links 35 and 36 rigidly joined to shaft 22 are equivalent to the triangular member 30 of Fig. 1. It is to be noticed that the locus of point D, the product point, is in the present invention a circle, the radius of which is determined by the length of link 35. Since it is only the relative dimension of the various linkages that are critical, the X input section may be dimensioned in terms of a unit A, the Y input section and guiding section in terms of a unit B, and the output section in terms of a unit C, as illustrated in Figs. 3, l, and 5. Further referring to Fig. 2, it is observed that if shafts 2| were temporarily severed and the members associated with framework M were rotated about an axis through shafts 2| with respect to the members associated with framework N, and the shaft rejoined, the computer would still function as before. The only requirement is that when X is'zero, angle G (as defined in Figs. 2 and 3) must be 20. Similarly, the absolute value of the angle between the members 35 and 36 as shown in Fig. 2 is not essential. The only requirement is that when the X and Y inputs equal zero, the XY scale must read zero. The zero position of the output section is illustrated in Fig. 5.

The relative dimensions of the X-input, Y- input, and. XY-output sections in terms of factors A, B and C respectively, are as hereafter stated. Referring to Fig. 3, the dimensions of member 21, which is fixedly secured to shaft 2| may be given as the letter A. The length of member 27A is purely arbitrary and may be chosen to be any convenient dimension.

Referring to Fig. 4, the critical relative dimension of the Y input and guiding sections, which are given in terms of a unit of measurement B, are as follows:

Vertical distance from pivot point A to pivot point B Horizontal distance from pivot point A to pivot point B .1508B to the left 3. 37113 above The length of member 28 3.5003 The length of member 32 1.500B The length of member 3| 3.5003 The length of member 33 3.5003 The length of member 35 1.050B

The relative dimensions of the output sections of the computer are shown in Fig. 5 in terms of a unit of measurement C. They are as follows:

.5130B below Thelength of frame ID from pivot point I B to pivot point C 3.7991C The length of member 36 1.50000 The length of member All from point C to I point J 1.70000 The length of member 40 maybe designated by the letter R.

"The length of member 1a 4.5 0090 As previously stated, the displacement of the XY slide is proportional to the product of the displacements of the X and Y sliders Nos. 25 and 50, respectively. Any convenient scales-may be used on the X and Y sliders and the output scale will ,be determined thereby. The range of best precision over which-the device operates, may be stated as follows:

The travel of the X input member should not ones-poo eiceea negitnvei-135h nor-exceed positives 35s,

that is, the total range of travel of the X input member'should riot-exceed .70A, where A is the length of link 2] and X is the actual X input, that is, the linear "horizontal displacement of min .119"; which is a closcap roximation of the horizontal component of displacement of point H. Similarly, the Y input should be limited so that Y is not "lessf'than zero, nor more than 1.668, whererY is the actual displacement of slider 50 land lllt issthev dimensional unit for the members sho'wri ini-Fige l. The range for the output section will be, determined by the input range. When the linkage'is' operated over this prescribed rangg theaverage error of the output over this 1 mange, which is uniformly distributed, is approximately ".15%, The actual XYoutput in terms of the horizontal component of displacement of pin I9 is equal to .8831R times the product of the actual X and Y input displacement.

It is to be understood that various changes and modifications may be made in this invention without departing from the spirit and scope thereof as set forth in the appended claims.

What is claimed is.

1. A mechanical computer for determining the product of two independent variables, one of which may be either positive or negative and the other which is positive in sign, said computer comprising a support, first, second, and third swinging members pivotally mounted on said support, first, second, and third slide members slidably mounted on said support, a first link operatively connecting said first slide member and said first swinging member, second and third links operatively connecting said second slides and said second swinging member, a fourth link operatively connecting said first swinging memher and the junction point of said second and third links, a fifth link operatively connecting said second and third swinging members, and a sixth link operatively connecting said third slide member and said third swinging member, said links and said swinging members having the following relative orientation and dimensions where the basis of comparison is taken as unity (1) Length of said first swinging member from the pivot point thereof to the point of connection of said fourth link 3. 5000 Length of said second link Length of said third link Length of said fourth link. Length of said fifth link Length of said second swinging member from the pivot point thereof to the point of connection of said third link. Length of said second swinging member from the pivot point thereof to the point of connection of said fifth link.. Angle included between the lines drawn from the pivot point of said second swinging member and the points of connection thereto of said third and fifth links Angle included between lines drawn from the pivot point of said first swinging member and the points of connection thereto of said first and fourth links Distance from the pivoted mounting of said third swinging lmelrnber to the point of connection thereto of said fifth 1 70 m Vertical distance between the pivot points of said first and second swinging members 3. 2371 Horizontal distance between the pivot points of said first and second swinging members .1508 Horizontal distance between the pivot points of said second and third swinging members 3. Vertical distance between the pivot points of said second and third swinging members 2124 Vertical distance between the pivoted connection of said second link to said second slide member and the pivot point of said first swinging member 5130 Length of said third swinging member the pivotal mountings described above providing a displacement of said third slide member which is directly proportional to the product of the displacements of said first and second slide members, the proportion constant being .8831R.

2. A mechanical computer for determining the algebraic product of two independent variables X and Y; of which X may be eitherpositive or negative and Y is positive in sign, said computer comprising,- asupport including a standard having an integral arm positioned coplanarly therewith and perpendicularlyv thereto, a triangular swinging member pivotally mounted at an apex on said standard'in substantially coplanar relationship with said support, and X-input slide operatively connected to a first unpivoted apex of said'triangula-r-swinging member such that transverse movement of said X-input slide causes rotation of said triangular swinging member-"about its piv0t:p0int,.- said X-input-slide having a scale calibratedinipositive .and negative values, on either side of :a'zero position and being arranged such that Is'aidslide is atsaid zero. position, when ia line connecting the: pivot. point and-said first apex of said triangular swinging member is coincident with a line drawn through said pivot point parallel to the axis of said standard, a bellcrank member pivotally mounted on said standard in substantially coplanar relationship with said support, a Y-input slide member mounted on said support for movement along a scale transversely of the axis of said standard, said scale being uniformly graduated in positive values of Y from a zero position at an end of said scale, a linear swinging member pivotally mounted on said integral arm in substantially coplanar relationship with said support, a first link pivotally attached to a second unpivoted apex of said triangular member, a second link pivotally attached at one end to said Y-input slide member and at the other end to the free end of said first link, a third link pivotally attached at one end to a first unpivoted end of said bell-crank member and at the other end to the junction of said first and second links, a fourth link pivotally attached at one end to the second unpivoted end of said bell-crank member and at the other end to a point on said linear swinging member, and an XY-output slide operatively connected to the unpivoted end of said linear swinging member, a scale positioned adjacent said XY output slide being uniformly calibrated in positive and negative values on either side of a zero position, said scale being arranged such that said XY-output slide is at said zero position when the axis of said linear swinging member is coincident with a line drawn through the pivot point of said linear swinging member which is parallel to the axis of said standard, said links and said swinging members having the following relative dimensions where the basis of comparison is taken as unity (1),

Length of said triangular swinging member from the pivot point thereof to the said second unpivoted apex thereof 3. 500 Length of said first link... 3, 500 Length of said second link 1 500 Length of said third link.. 3. 500 Length of said fourth link 4. 500 Length of said linear swinging member R, R being gr7eiger than Length of said linear swinging member from the pivot point thereof to the point of connection of said fourth link thereto 1 Length of said bell-crank member from the pivot point thereof to the said first unpivoted end thereof .c l 050 Length of said bell-crank member from the pivot point thereof to the said second unpivoted end thereof. 1.500 Angle included between lines drawn from the pivot point of said bell-erank member and the said first and second unpivoted ends thereof Angle included between lines drawn from the pivot point of said triangular swinging member to the said first and second unpivoted apiees thereof 20 Distance along the axis of said standard between the pivot points of said triangular and said bell-crank swinging members 3. 2371 Distance transversely of the axis of said standard between the pivot points of said triangular and said bell-crank swinging members .1508

"Distance transversely of the Distance along the axis of said standard betwens'aid 'Y-input slide and thetpivot-point of said triangular swinging member 5130 tween said zero point on said v input scale and the pivot point of said triangnlar swinging member 1. 4095 Distance transversely of the axis of said standard between the pivot points of said bell-crank swinging member and said linear swinging member u 3. 7991 Distance along the axis of saidstandard between the pivot points of said bell-crank swinging member and said linear swinging member .2124 Range of movement of said X input slide member io best precision Range of movement of said 'best precisiont XY-output scale factor.

ut slide member for the. aforementioned dimensions and orientation providing a displacement of said XY-output slide member which is directly proportional to the 15 Number product of the displacements of said X-input and said Y-input members with an average error of range of best precision. 4 ANTONIN SVOBODA.

.. REFERENCES CITED The following references are of record inthe file of this patent:

UNITED STATES PATENTS v 10 Number Name Date 1 2,229,156 Wertheimer Jan. 21, 1941 2,394,180 Imm Feb; 5, 1946 FOREIGN PATENTS I Country D t 113,136 Great Britain Feb. 7, 1918 291,556 Italy Dec. 19, 1931 

